Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole
ISBN 10:
ISBN 13:

Chapter 10 - Section 10.6 - The Three-Dimensional Coordinate System - Exercises - Page 482: 39

Answer

$A = 1257$ $V = 4189$

Work Step by Step

We can write the general equation of a sphere: $(x-a)^2+(y-b)^2+(z-c)^2 = r^2$ where $(a,b,c)$ is the center of the sphere and $r$ is the radius The equation of the sphere is: $x^2+y^2+z^2 = 100$ The center of the sphere is $(0,0,0)$ The radius of the sphere is $10$ We can find the surface area: $A = 4~\pi~r^2$ $A = (4~\pi)~(10)^2$ $A = 400~\pi$ $A = 1257$ We can find the volume: $V = \frac{4}{3}~\pi~r^3$ $V = \frac{4}{3}~\pi~(10)^3$ $V = 4189$
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